What is the area bounded by the curves, the lines x = 0 and x = 1 ?
For the next two (02) items that follow : Consider the curves \( y = x^2 \) and \( y = 2|x| \).
- A. 1 square unit
- B. \frac{2}{3} square unit ✓
- C. \frac{1}{2} square unit
- D. \frac{1}{3} square unit
Correct Answer: B. \frac{2}{3} square unit
Explanation
In the interval, \( 2|x| = 2x \) and it lies above \( x^2 \). The required area is \( \int_0^1 (2x - x^2) dx = \left[x^2 - \frac{x^3}{3}\right]_0^1 = 1 - \frac{1}{3} = \frac{2}{3} \) square units.
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